Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations

Weighted Block Runge-Kutta (WBRK) methods are derived to solve first order stiff ordinary differential equations (ODEs). The proposed methods approximate solutions at two points concurrently in a block at each step. Three sets of weight are chosen and implemented to the WBRK methods. Stability regions of the WBRK methods with each set of weight are constructed by using MAPLE14. Stability properties of the proposed methods with each weight show that the methods are suitable for solving stiff ODEs. Numerical results are presented and illustrated in the form of efficiency curves. Performances of the WBRK methods in terms of maximum error and computational time are compared with the third order Runge-Kutta (RK3) and the modified weighted RK3 method based on centroidal mean (MWRK3CeM). These methods are tested with problems of single and system of first order stiff ODEs. Comparison of the proposed methods between sets of weight is also analyzed. The numerical results are obtained by using MATLAB R2011a. Numerical results generated show that the WBRK methods obtained better accuracy and less computational time than the RK3 and MWRK3CeM method.

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